Neural implicit 3D representations have emerged as a powerful paradigm for
reconstructing surfaces from multi-view images and synthesizing novel views.
Unfortunately, existing methods such as DVR or IDR require accurate per-pixel
object masks as supervision. At the same time, neural radiance fields have
revolutionized novel view synthesis. However, NeRF's estimated volume density
does not admit accurate surface reconstruction. Our key insight is that
implicit surface models and radiance fields can be formulated in a unified way,
enabling both surface and volume rendering using the same model. This unified
perspective enables novel, more efficient sampling procedures and the ability
to reconstruct accurate surfaces without input masks. We compare our method on
the DTU, BlendedMVS, and a synthetic indoor dataset. Our experiments
demonstrate that we outperform NeRF in terms of reconstruction quality while
performing on par with IDR without requiring masks.

该研究通过统一的方式制定了表面和体渲染，从而使得无需任何输入蒙版即可实现准确表面重建，并通过实验证明其能够在各方面都优于 NeRF 方法并与 IDR 方法相媲美。

UNISURF：统一神经隐式曲面和辐射场用于多视角重建

UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for  Multi-View Reconstruction

In this paper we develop algorithms for approximating matrix multiplication
with respect to the spectral norm. Let A\in{\RR^{n\times m}} and B\in\RR^{n
\times p} be two matrices and \eps>0. We approximate the product A^\top B using
two down-sampled sketches, \tilde{A}\in\RR^{t\times m} and
\tilde{B}\in\RR^{t\times p}, where t\ll n such that \norm{\tilde{A}^\top
\tilde{B} - A^\top B} \leq \eps \norm{A}\norm{B} with high probability. We use
two different sampling procedures for constructing \tilde{A} and \tilde{B}; one
of them is done by i.i.d. non-uniform sampling rows from A and B and the other
is done by taking random linear combinations of their rows. We prove bounds
that depend only on the intrinsic dimensionality of A and B, that is their rank
and their stable rank; namely the squared ratio between their Frobenius and
operator norm. For achieving bounds that depend on rank we employ standard
tools from high-dimensional geometry such as concentration of measure arguments
combined with elaborate \eps-net constructions. For bounds that depend on the
smaller parameter of stable rank this technology itself seems weak. However, we
show that in combination with a simple truncation argument is amenable to
provide such bounds. To handle similar bounds for row sampling, we develop a
novel matrix-valued Chernoff bound inequality which we call low rank
matrix-valued Chernoff bound. Thanks to this inequality, we are able to give
bounds that depend only on the stable rank of the input matrices...

本文提出了一种利用两种不同抽样方法进行矩阵乘法，以逼近具有谱范数的矩阵，从而得出理论上的界限。